HSC Commerce (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Solve the differential equation (x² – yx²)dy + (y² + xy²)dx = 0

Solve: `("d"y)/("d"x) + 2/xy` = x² 

For the differential equation, find the particular solution (x – y²x) dx – (y + x²y) dy = 0 when x = 2, y = 0

Solve the following differential equation

`yx ("d"y)/("d"x)` = x² + 2y² 

For the differential equation, find the particular solution

`("d"y)/("d"x)` = (4x +y + 1), when y = 1, x = 0

Solve the following differential equation y²dx + (xy + x²) dy = 0

Choose the correct alternative :

Which of the following statement is true?

Choose the correct alternative :

Which of the following is not a statement?

The dual of the statement (p ˅ q) ˄ (r ˅ s) is ______.

State whether the following statement is True or False:

p → q is equivalent to p → ~ q

State whether the following statement is True or False:

Truth value of `sqrt(3)` is not an irrational number is F

State whether the following statement is True or False:

(p ˅ q) ˄ ~ p is a contradiction

State whether the following statement is True or False:

p ↔ q is false when p and q have different truth values

State whether the following statement is True or False:

The dual of (p ˄ q) ˅ ~ q is (p ˅ q) ˄ ~ q

State whether the following statement is True or False:

Mathematical identities are true statements

State whether the following statement is True or False:

p ˅ ~ p ≡ ~ c

The truth value of negation of “London is in England” is ______

The truth value of the statement “Neither 27 is a prime number nor divisible by 4” is ______

Using truth table prove that ~ p ˄ q ≡ ( p ˅ q) ˄ ~ p

Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r).